Lump and new interaction solutions of the (3+1)-dimensional generalized Shallow Water-like equation along with chaotic analysis

In recent years, interest in nonlinear evolution equations has surged, underscoring their critical role in understanding complex dynamic systems. This work focuses on the (3+1)-dimensional generalized shallow water-like equation, especially for its relevance to nonlinear wave phenomena. Using Hirota bilinear method, we derive lump solutions for this equation and innovatively explore the interaction dynamics between these lumps and the Weierstrass elliptic function. Additionally, we analyze chaotic solutions for lumps derived from the Duffing chaotic system, examining their chaotic structures in detail. The physical characteristics of these solutions are illustrated via three-dimensional profiles and their corresponding two-dimensional plots. Our findings reveal that the methods employed are both efficient and effective, providing valuable insights into the dynamics of mathematical physics equations.